The author criticizes Bourbaki’s approach to fundamentals of mathematics, logic and set theory. He believes that despite being already aware of the impact of Gödel’s proof on Hilbert’s program of formalism, the group deliberately chose to ignore it, so far as they even refused to mention Gödel and address his work. He then points out the difference between arithmetic and geometric aspects of mathematics, and suggests that Zermelo’s set theory, which was acknowledged by Bourbaki, suffices only for the geometric part whereas the arithmetic side needs to rely on Zermelo-Fraenkel system of axioms.
